The study of minimum-norm interpolating algorithms has mainly been investigated in three settings so far. The first line of research has focused on a random matrix regime where the number of data points and parameters are proportional. Here precise asymptotic results can be obtained, see for instance [1]}, [2]} for max-\(\ell _2\) -margin interpolation, [3]} for max-\(\ell _1\) -margin interpolation and consequently AdaBoost, [4]} for 2-layer-neural networks in regression and [5]} for minimum-\(\ell _2\) -norm linear regression. However, these results do not exploit possible low-dimensional structure such as sparsity and they also require a large enough, constant, noise-level, leading to inconsistent estimators.
